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The influence of random phase errors on the angular resolution of a focused synthetic aperture radar system is treated. The principal measure of performance has been taken as the mean envelope power at the system output. This system output power is evaluated exactly, although not in closed form, based on the following assumptions: 1) the real beam pattern is Gaussian; 2) the random phase error is essentially a geometry-independent ergodic process with a Gaussian amplitude distribution and zero mean; and 3) the random phase error has a Gaussian correlation function. The curves presented in this paper can be used to estimate expected system power response, expected system resolution and effective aperture length beyond which, in the presence of phase error, little gain in resolution is expected. It was found that multiple sources of error with different correlation intervals make explicit solution of the integral equation for system power response practically impossible. In this situation, a reasonable approach is to evaluate the system power response separately for each error. If one of the errors is clearly dominant, it may be regarded as bounding achievable performance.